1. Field of the Invention
This invention generally relates to digital communications and, more particularly, to systems and methods for minimizing the effects of inter-symbol interference in a non-return to zero (NRZ) data channel when the noise distribution is asymmetric.
2. Description of the Related Art
FIG. 1 is a diagram illustrating a signal recovered from a binary symmetric, non-dispersive channel in the presence of symmetric noise (prior art). Conventionally, the signal is filtered with a transfer function matched to the signaling waveform (in this case a one unit step) and thresholded at the voltage level most likely to yield the transmitted bit. To recover the transmitted information, a hard decision must be made as to the value of the received bit.
As a function of the filtering process, and sometimes as a result of the transmission process, pulse spreading occurs. That is, the energy associated with a bit spreads to neighboring bits. For small degrees of spreading these effects of this can be limited to the nearest neighbors with modest degradation in performance.
Three basic types of pulse spreading exist. The first possibility is that both the neighboring bits are a zero (no neighboring bits are a one). The second possibility is that only one of the neighboring bits (either the preceding or subsequent bit) is a one. Alternately stated, only one of the neighboring bits is a zero. The third possibility is that both neighboring bits are one. For each of these cases the likelihood of error in determining a bit value can be minimized if a different thresholds are used for different bit combinations.
FIG. 2 is a diagram illustrating received waveforms that are distorted in response to the inter-symbol interference resulting from energy dispersion (prior art). The value at the output of the filter varies with each bit, and is essentially a random process, due to the non-deterministic nature of the information, and pseudorandom scrambling that is often used in the transmission of NRZ data streams. However, received bits can be characterized with probability density functions, as shown. Without knowledge of the neighboring bits, a single probability density function can be extracted that represents the random behavior of the input over all conditions and all sequences. However, conditional probability density functions can be defined for the three cases mentioned above. Namely, probability density functions can be defined for the cases where there are zero neighboring ones, only one neighboring one, and two neighboring ones.
If the bit value decision process could be made using the knowledge of the decision made on the preceding decoded bit, and with a measurement of a subsequent decoded bit, then the corresponding probability density function could be selected to make a more accurate decision on the current bit decision. However, the cost and accuracy of conventional analog-to-digital (A/D) conversion circuits make such a solution impractical.
The degree of dispersion exhibited by a channel, and hence the separation of the conditional probability density functions, varies in response to a number of fixed and variable factors. Effective dispersion mitigation techniques must therefore be easily optimized to the channel and somewhat adaptive to changes in the channel due to aging, temperature changes, reconfiguration, and other possible influences.
The above-mentioned problems, in separating the conditional probability density functions of the three bit sequence scenarios, are exasperated when the noise distribution is not symmetric. That is, the energy distributions for “1” bits and “0” bits are different.
FIG. 3 is a diagram illustrating a signal recovered from a binary symmetric, non-dispersive channel in the presence of asymmetric noise (prior art). There are differences in the shapes of the “1” and “0” probability density functions. Because of the overlap of the two functions, the values of thresholds V1′ and V0′ are not necessarily the same as the values of thresholds V1 and V0 in FIG. 1.
It would be advantageous if inter-symbol interference (ISI) caused by energy dispersion in a received NRZ data channel could be minimized.
It would be advantageous if the bit decision thresholds could be modified to take account of the dispersed energy in the neighboring bits in the NRZ data stream.
It would be advantageous if the above-mentioned inter-symbol interference modifications could also take into account the effects of an asymmetric noise distribution.